Physics H133: Problem Set #2
Here are some hints, suggestions, and comments on the problem set.
Remember to give a good explanation, no longer than
- Q2B.8: Is a deep voice dominated by long or short wavelengths?
How about a high voice? What does the wavelength have to do
with how well the sound carries around a corner?
- Q2S.4: You would not hear music where the sound waves from the
two speakers are exactly out of phase. Where does this happen if
you've reversed the wires? Would the waves be out of phase everywhere
in the room?
Chapter Q2 Problems
- Q2S.1: Is this diffraction or two-slit interference? Again,
draw a good picture! Be careful of whether you want constructive
or destructive interference for the different parts of the problem.
- Q2S.6: Why do the sound waves spread? Within what angle is
most of the sound power concentrated? If it widens 5m in
traveling 100m, what is the corresponding angle? (It helps to draw
a picture!) Remember that the speed of sound is about 343 m/s.
- Q2S.7: This is similar to Q2S.6. Draw a good picture so
you can identify the appropriate angle in terms of how far away you
are and how far you walk past the door. To what does the partially
open door correspond?
- Q2A.1: At angle theta, what is the extra path length that one
of the waves takes compared to the other? You can use this to find
the phase difference Phi between the waves (Phi/2 pi = path
difference/wavelength). Write waves from slits one and two so
that they are out of phase by Phi and then add them together, using
trig identities for the sin of a sum or difference of angles.
It's easiest (by far) to split the path difference of Phi between
the two waves, assigning +Phi/2 to one and -Phi/2 to the other.
- Q2R.1: Think about this as a two-slit interference problem,
where you are locating places where the interference is totally
constructive or destructive, based on path differences.
(But note that the sounds are not actually interfering; it is only
the timing of when the foghorn sounds you care about.)
Your comments and
suggestions are appreciated.
Physics H133: Hints for Problem Set 2.
Last modified: 08:26 pm, March 27, 2012.